acta physica slovaca 

Acta Physica Slovaca 60, No.4, 393495 (2010) (103 pages)
POSTNEWTONIAN REFERENCE FRAMES FOR ADVANCED THEORY OF THE LUNAR MOTION AND FOR A NEW GENERATION OF LUNAR LASER RANGING Yi Xie^{1,2} and Sergei Kopeikin^{2} ^{1}Astronomy Department, Nanjing University, Nanjing, Jiangsu 210093, China ^{2}Department of Physics & Astronomy, University of Missouri, Columbia, Missouri 65211, USA Full text: ::pdf :: (Received 03 June 2010, accepted 10 June 2010) Abstract: We overview a set of postNewtonian reference frames for a comprehensive study of the orbital dynamics and rotational motion of Moon and Earth by means of lunar laser ranging (LLR). We employ a scalartensor theory of gravity depending on two postNewtonian parameters, and , and utilize the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. We assume that the solar system is isolated and spacetime is asymptotically flat at infinity. The primary reference frame covers the entire spacetime, has its origin at the solarsystem barycenter (SSB) and spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are forming the International Celestial Reference Frame (ICRF). The secondary reference frame has its origin at the EarthMoon barycenter (EMB). The EMB frame is locallyinertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames geocentric (GRF) and selenocentric (SRF) have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically nonrotating local frames is in a more simple mathematical description. Each local frame can be aligned with the axes of ICRF after applying the matrix of the relativistic precession. The set of one global and three local frames is introduced in order to fully decouple the relative motion of Moon with respect to Earth from the orbital motion of the EarthMoon barycenter as well as to connect the coordinate description of the lunar motion, an observer on Earth, and a retroreflector on Moon to directly measurable quantities such as the proper time and the roundtrip laserlight distance. We solve the gravity field equations and find out the metric tensor and the scalar field in all frames which description includes the postNewtonian multipole moments of the gravitational field of Earth and Moon. We also derive the postNewtonian coordinate transformations between the frames and analyze the residual gauge freedom. DOI: 10.2478/v1015501000040 PACS: 04.20.Gz, 04.80.y, 95.55.Br, 96.15.Vx Keywords: Relativity, Gravitation, Gravitomagnetism, Gauge invariance, Brans Dicke theory, PostNewtonian celestial mechanics, Reference frames, EarthMoon system, Lunar laser ranging 
ISSN 1336040X (online) ISSN 03230465 (printed) For authors: ActaStyle.cls 
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